Choosing within application documents
The terms overlap, so start with what your program asks. In US graduate admissions, a statement of purpose focuses on academic preparation, research interests and fit, and a separate personal statement or personal history statement may ask about background and motivation. In the UK, the undergraduate personal statement is submitted once through UCAS for up to five courses, while UK postgraduate programs often use "personal statement" to mean something closer to a statement of purpose. Many European programs ask for a motivation letter, and faculty-facing applications may add a research statement or a statement on contributions to diversity or community.
The supporting documents matter as much as the essays. A CV should provide the evidence your statement refers to, and recommendation letters should confirm your strengths from someone else's perspective. We work on the documents together where possible so they reinforce one another instead of repeating the same points.